Learn Koopman and Transfer operators for Dynamical Systems and Stochastic Processes

kooplearn is a Python library designed for learning Koopman or Transfer operators associated with dynamical systems. Given a nonlinear dynamical system $x{t + 1} = S(x{t})$, the Koopman operator provides a global linearization of the dynamics by mapping it to a suitable space of observables $\mathcal{F}$. An observable is any (scalar) function of the state. The Koopman operator $\mathsf{K}$ is defined as $$(\mathsf{K}f)(x{t}) = f(x{t + 1}) := f \circ S (xt) \qquad f \in \mathcal{F}.$$ Similarly, given a stochastic process $X:= { X{s} \colon s \in \mathbb{N}}$, its *Transfer operator returns the expected value of any observable forward in time. The Transfer operator $\mathsf{T}$ is defined as $$(\mathsf{T}f)(x) := \mathbb{E}\left[f(X{t + 1}) \mid X{t} = x \right] \qquad f \in \mathcal{F}.$$

kooplearn provides a suite of algorithms for model training and analysis, enabling users to perform forecasting, spectral decomposition, and modal decomposition based on the learned operator.

Please note that kooplearn is currently under active development, and while we are continuously adding new features and improvements, some parts of the library might still be a work in progress.

Features

• Implement different algorithms to learn Koopman or transfer operators for dynamical systems.
• Perform forecasting using the learned operators.
• Conduct spectral decomposition of the learned operator.
• Perform modal decomposition for further analysis.

Installation

To install the core version of kooplearn, without optional dependencies, run

   pip install kooplearn

To install the full version of kooplearn, including Neural-Network models, and the dahsboard, run

   pip install "kooplearn[full]"

To install the development version of kooplearn, run

   pip install --upgrade git+https://github.com/Machine-Learning-Dynamical-Systems/kooplearn.git

Contributing

We welcome contributions from the community! If you're interested in contributing to kooplearn, please follow these steps:

1. Fork the repository on GitHub.
2. Clone your forked repository to your local machine.
3. Create a new branch for your feature or bug fix: git checkout -b feature/your-feature-name or git checkout -b bugfix/issue-number.
4. Make your changes and commit them with descriptive commit messages.
5. Push your changes to your forked repository.
6. Create a pull request from your branch to the main branch of the original repository.
7. Provide a clear title and description for your pull request, including any relevant information about the changes you've made.

We appreciate your contributions and will review your pull request as soon as possible. Thank you for helping improve kooplearn!

License

This project is licensed under the MIT License.

Main contributors

kooplearn is an joint effort between teams at the Italian Institute of Technology in Genoa and the École polytechnique in Paris. The main contributors to the project are (in alphabetical order):

• Vladimir Kostic
• Karim Lounici
• Giacomo Meanti
• Erfan Mirzaei
• Pietro Novelli
• Daniel Ordonez
• Grégoire Pacreau
• Massimiliano Pontil
• Giacomo Turri

The mantainer of this repo is Pietro Novelli.

We hope you find kooplearn useful for your dynamical systems analysis. If you encounter any issues or have suggestions for improvements, please don't hesitate to raise an issue. Happy coding!